Abstract: Based on three different forms of the series solutions of the vibrating string equation under the definite

condition，the truncation error of the series solutions is discussed in two different conditions，ignoring or not ignoring

the independent variables. When the independent variables，by estimating the general truncation error，defining

the Gibbs-like phenomenon is considered，we obtain the estimation of the maximum value of the truncation error.

Key words: vibrating string equation, truncation error, Gibbs-like phenomenon